Irreducible Modules of Finite Dimensional Quantum Algebras of type A at Roots of Unity

Details Irreducible Modules of Finite Dimensional Quantum Algebras of type A at Roots of Unity Irreducible Modules of Finite Dimensional Quantum Algebras of type A at Roots of Unity

2001-03-05

arxiv.org/abs/math/0103021v1

Mathematics

Quantum Algebra

LaTeX(2e), 17 pages

Scientific paper

10.1063/1.1453498

Specializing properly the parameters contained in the maximal cyclic representation of the non-restricted A-type quantum algebra at roots of unity, we find the unique primitive vector in it. We show that the submodule generated by the primitive vector can be identified with an irreducble highest weight module of the finite dimensional A-type quantum algebra which is defined as the subalgebra of the restricted quantum algebra at roots of unity.

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